vegdist                package:vegan                R Documentation

_D_i_s_s_i_m_i_l_a_r_i_t_y _I_n_d_i_c_e_s _f_o_r _C_o_m_m_u_n_i_t_y _E_c_o_l_o_g_i_s_t_s

_D_e_s_c_r_i_p_t_i_o_n:

     The function computes dissimilarity indices that are useful for or
     popular with community ecologists. Gower, Bray-Curtis, Jaccard and
     Kulczynski indices are good in detecting underlying ecological
     gradients (Faith et al. 1987). Morisita and Horn-Morisita indices
     should be able to handle different sample sizes (Wolda 1981, Krebs
     1999), and Mountford (1962) index for presence-absence data should
     be able to handle unknown (and variable) sample sizes.

_U_s_a_g_e:

      vegdist(x, method="bray", diag=FALSE, upper=FALSE) 

_A_r_g_u_m_e_n_t_s:

       x: Community data matrix.

  method: Dissimilarity index, partial match to  '"manhattan"',
          '"euclidean"', '"canberra"', '"bray"', '"kulczynski"',
          '"jaccard"', '"gower"', '"morisita"', '"horn"' or
          '"mountford"'.

    diag: Compute diagonals. 

   upper: Return only the upper diagonal. 

_D_e_t_a_i_l_s:

     Jaccard and Mountford indices are discussed below. The other
     indices are defined as:

       'euclidean'   d[jk] = sqrt(sum (x[ij]-x[ik])^2)
       'manhattan'   d[jk] = sum(abs(x[ij] - x[ik]))
       'gower'       d[jk] = sum (abs(x[ij]-x[ik])/(max(x[i])-min(x[i]))
       'canberra'    d[jk] = (1/NZ) sum ((x[ij]-x[ik])/(x[ij]+x[ik]))
                     where NZ is the number of non-zero entries.
       'bray'        d[jk] = (sum abs(x[ij]-x[ik])/(sum (x[ij]+x[ik]))
       'kulczynski'  d[jk] 1 - 0.5*((sum min(x[ij],x[ik])/(sum x[ij]) + (sum min(x[ij],x[ik])/(sum x[ik]))
       'morisita'    {d[jk] = 2*sum(x[ij]*x[ik])/((lambda[j]+lambda[k]) * sum(x[ij])*sum(x[ik]))  }
                     where lambda[j] = sum(x[ij]*(x[ij]-1))/sum(x[ij])*sum(x[ij]-1)
       'horn'        Like 'morisita', but lambda[j] = sum(x[ij]^2)/(sum(x[ij])^2)

     Jaccard index is computed as 2B/(1+B), where B is Bray-Curtis
     dissimilarity.

     Mountford index is defined as M = 1/alpha where alpha is the
     parameter of Fisher's logseries assuming that the compared
     communities are samples from the same community (cf. 'fisherfit',
     'fisher.alpha'). The index M is found as the positive root of
     equation exp(a*M) + exp(b*M) = 1 + exp((a+b-j)*M), where j is the
     number of species occurring in both communities, and a and b are
     the number of species in each separate community (so the index
     uses presence-absence information). Mountford index is usually
     misrepresented in the literature: indeed Mountford (1962)
     suggested an approximation to be used as starting value in
     iterations, but the proper index is defined as the root of the
     equation above. The function 'vegdist' solves M with the Newton
     method. Please note that if either a or b are equal to j, one of
     the communities could be a subset of other, and the dissimilarity
     is 0 meaning that non-identical objects may be regarded as similar
     and the index is non-metric. The Mountford index is in the range 0
     ... log(2), but the dissimilarities are divided by log(2)  so that
     the results will be in the conventional range 0 ... 1.

     Morisita index can be used with genuine count data only. Its
     Horn-Morisita variant is able to handle any abundance data.

     Euclidean and Manhattan dissimilarities are not good in gradient
     separation without proper standardization but are still included
     for comparison and special needs.

     Bray-Curtis and Jaccard indices are rank-order similar, and some
     other indices become identical or rank-order similar after some 
     standardizations, especially with presence/absence transformation
     of equalizing site totals with 'decostand'.

     The naming conventions vary. The one adopted here is traditional
     rather than truthful to priority. The abbreviation '"horn"' for
     the Horn-Morisita index is misleading, since there is a separate
     Horn index. The abbreviation will be changed if that index is
     implemented in 'vegan'.

_V_a_l_u_e:

     Should provide a drop-in replacement for 'dist' and return a
     distance object of the same type.

_N_o_t_e:

     The  function is an alternative to 'dist' adding some ecologically
     meaningful indices.  Both methods should produce similar types of
     objects which can be interchanged in any method accepting either. 
     Manhattan and Euclidean dissimilarities should be identical in
     both methods, and Canberra dissimilarity may be similar.

_A_u_t_h_o_r(_s):

     Jari Oksanen

_R_e_f_e_r_e_n_c_e_s:

     Faith, D. P, Minchin, P. R. and Belbin, L. (1987). Compositional
     dissimilarity as a robust measure of ecological distance.
     _Vegetatio_ 69, 57-68.

     Krebs, C. J. (1999). _Ecological Methodology._ Addison Wesley
     Longman.

     Mountford, M. D. (1962). An index of similarity and its
     application to classification problems. In: P.W.Murphy (ed.),
     _Progress in Soil Zoology_, 43-50. Butterworths.

     Wolda, H. (1981). Similarity indices, sample size and diversity.
     _Oecologia_ 50, 296-302.

_S_e_e _A_l_s_o:

     'decostand', 'dist', 'rankindex', 'isoMDS', 'stepacross'.

_E_x_a_m_p_l_e_s:

     data(varespec)
     vare.dist <- vegdist(varespec)
     # Orlci's Chord distance: range 0 .. sqrt(2)
     vare.dist <- vegdist(decostand(varespec, "norm"), "euclidean")

